Not sure really where to start Let TAR3 rightarrow R2 be the

Not sure really where to start

Let TA:R3 rightarrow R2 be the matrix transformation associated with a matrix A, and suppose that TA(1,1,0) = (3,-7), TA(1,-1,0) = (5,9), TA( 1,1,1) = (6,-4). Find the matrix A.

Solution

The final matrix is equal to (2X1)

Hence the matrix A must be of order 2 X 3 so when multiplied by 3X1 vector will result into 2X1 vector

using the first relation we get

From first relation

a + b = 3

d + e = -7

From second relation

a - b = 5

d - e = 9

From third relation

a + b + c = 6

d + e + f = -4

We get after solving these 6 equations, the values as follows

a = 4, b = -1

d = 1, e = -8

c = 3, f = 3

Hence the A matrix which is 3X2 matrix is equal to

a	b	c
d	e	f